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Détails
| Format : | Livre |
|---|---|
| Tous les auteurs / collaborateurs : |
M G Papadopoulos; Andrzej J Sadlej; J Leszczynski |
| ISBN : | 9781402048494 1402048491 9781402048500 1402048505 |
| Numéro OCLC : | 318296029 |
| Contenu : | st1\:*{behavior:url(#ieooui) } /* Style Definitions */ /* Style Definitions */ $m? .-22 The case m = 2.- 23 TC(F($\mathbb{R}$m; n) in the case m $\geq$ 3 odd .- 24 Shade.-25 Illuminating the complement of the braid arrangement .-26 A quadratic motion planning algorithm in F($\mathbb{R}$m; n).-27 Configuration spaces of graphs.-28 Motion planning in projective spaces .-29 Nonsingular maps.- 30 TC(($\mathbb{R}$Pn) and the immersion problem.-31 Some open problems.- Application of Floer Homology of Langrangian Submanifolds to Symplectic Topology;K. Fukaya.- 1 Introduction.- 2 Lagrangian submanifold of $\mathbb{C}$n .-3 Perturbing Cauchy -- Riemann equation.- 4 Maslov index of Lagrangian submanifold with vanishing second Betti number.-5 Floer homology and a spectral sequence .-6 Homology of loop space and Chas -- Sullivan bracket .-7 Iterated integral and Gerstenhaber bracket.- 8 A$_\infty$ deformation of de Rham complex.- 9 S1 equivariant homology of loop space and cyclic A1 algebra .-10 L$_\infty$ structure on H(S1 $\times$ Sn; $\mathbb{Q}$).-11 Lagrangian submanifolds of $\mathbb{C}$3 .-12 Aspherical Lagrangian submanifolds .-13 Lagrangian submanifolds homotopy equivalent to S1 $\times$ S2m .-14 Lagrangian submanifolds of $\mathbb{C}$Pn .- The $\mathcal{LS}$-Index: A Survey; M. Izydorek.- 1 Introduction .-2 The $\mathcal{LS}$-index.-2.1 Basic definitions and facts.-2.2 Spectra .-2.3 The $\mathcal{LS}$-index .- 3 Cohomology of spectra .-4 Attractors, repellers and Morse decompositions .- 5 Equivariant $\mathcal{LS}$-flows and the G-$\mathcal{LS}$-index.-5.1 Symmetries.-5.2 Isolating neighbourhoods and the equivariant $\mathcal{LS}$-index .-6 Applications.-6.1 A general setting .-6.2 Applications of the $\mathcal{LS}$-index .-6.3 Applications of the cohomological $\mathcal{LS}$-index .-6.4 Applications of the equivariant LS-index.- Lectures on Floer Theory and Spectral Invariants of Hamiltonian Flows; Y.-G. Oh.- 1 Introduction .-2 The free loop space and the action functional.-2.1 The free loop space and the S1-action in general.-2.2 The free loop space of symplectic manifolds.-2.3 The Novikov covering.-2.4 Perturbed action functionals and their action spectra.-2.5 The L2-gradient flow and perturbed Cauchy -- Riemann equations.-2.6 Comparison of two Cauchy -- Riemann equations.-3 Floer complex and the Novikov ring.-3.1 Novikov -- Floer chains and the Novikov ring.-3.2 Definition of the Floer boundary map.-3.3 Definition of the Floer chain map.-3.4 Semi-positivity and transversality.-3.5 Composition law of Floer's chain maps.-4 Energy estimates and Hofer's geometry.- 4.1 Energy estimates and the action level changes.-4.2 Energy estimates and Hofer's norm.-4.3 Level changes of Floer chains under the homotopy .-4.4 The $\epsilon$-regularity type invariants .-5 Definition of spectral invariants and their axioms.-5.1 Floer complex of a small Morse function.-5.2 Definition of spectral invariants.-5.3 Axioms of spectral invariants.-6 The spectrality axiom.-6.1 A consequence of the nondegenerate spectrality axiom.-6.2 Spectrality axiom for the rational case.-6.3 Spectrality for the irrational case.-7 Pants product and the triangle inequality.-7.1 Quantum cohomology in the chain level.-7.2 Grading convention.-7.3 Hamiltonian fibrations and the pants product .- 7.4 Proof of the triangle inequality.-8 Spectral norm of Hamiltonian diffeomorphisms.-8.1 Construction of the spectral norm.-8.2 The $\epsilon$-regularity theorem and its consequences.-8.3 Proof of nondegeneracy.-9 Applications to Hofer geometry of Ham(M;$\omega$).-9.1 Quasi-autonomous Hamiltonians and the minimality conjecture.- 9.2 Length minimizing criterion via $\rho$(H; 1).-9.3 Canonical fundamental Floer cycles.-9.4 The case of autonomous Hamiltonians.-10 Remarks on the transversality for general (M;$omega$).- A Proof of the index formula.- Floer Homology, Dynamics and Groups; L. Polterovich.-1 Hamiltonian actions of finitely generated groups.-1.1 The group of Hamiltonian diffeomorphisms.-1.2 The no-torsion theorem.-1.3 Distortion in normed groups .-1.4 The No-Distortion Theorem.-1.5 The Zimmer program.- 2 Floer theory in action.-2.1 A brief sketch of Floer theory .-2.2 Width and torsion.-2.3 A geometry on Ham(M;$\omega$).-2.4 Width and distortion.-2.5 More remarks on the Zimmer program.-3 The Calabi quasi-morphism and related topics.-3.1 Extending the Calabi homomorphism.-3.2 Introducing quasi-morphisms.-3.3 Quasi-morphisms on Ham(M;$\omega$).-3.4 Distortion in Hofer's norm on Ham(M;$\omega$).- 3.5 Existence and uniqueness of Calabi quasi-morphisms.-3.6 "Hyperbolic" features of Ham(M;$\omega$)? .-3.7 From $\pi$1(M) to Diff0(M;$\Omega$).- Symplectic topology and Hamilton -- Jacobi equations; C. Viterbo.- 1 Introduction to symplectic geometry and generating functions.-1.1 Uniqueness and first symplectic invariants.-2 The calculus of critical level sets.-2.1 The case of GFQI.-2.2 Applications.-3 Hamilton -- Jacobi equations and generating functions.-4 Coupled Hamilton -- Jacobi equations.-Index. |
| Titre de collection : | Challenges and Advances in Computational Chemistry and Physics. |
| Responsabilité : | M.G. Papadopoulos. |
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